Frequency Domain System Identification Research Articles

Data reduction using a generalized regressive discrete Fourier series

With the development of optical measurement techniques it is possible to obtain vast amounts of data. In vibrometry applications in particular operational deflection shapes are often obtained with very high spatial resolution. It has long been known that it is possible to reduce (approximate) the measurement data by means of a Fourier decomposition. One of the most common techniques for evaluating optical measurement data is by means of a Fourier analysis. It is well known that for periodic and band-limited sequences the Discrete Fourier Transform (DFT) returns the true Fourier coefficients when exactly 1 period (or a multiple) is processed. Leakage will occur when less than 1 period is considered. This gives rise to non-negligible errors, which can be resolved by using the Generalized Regressive Discrete Fourier Series (GRDFS), introduced in this article. The measured signal is represented by a model using sines and cosines. The coefficients of those sines and cosines are then estimated together with the phase and frequency on a global scale by means of a frequency domain system identification technique. By making use of the regressive technique proposed in this paper, it is possible to reduce the data in comparison to the classical Fourier decomposition by a sizeable factor. In this article the method will be applied in particular to the reduction of data for laser vibrometer measurements performed on an Inorganic Phosphate Cement (IPC) beam (1D), as well as on an aluminium plate (2D). The proposed technique will also be validated on both 1D and 2D simulations of varying complexity.

FREQUENCY DOMAIN SYSTEM IDENTIFICATION TOOLBOX FOR MATLAB: CHARACTERIZING NONLINEAR ERRORS OF LINEAR MODELS

System identification often means the determination of linear models from input-output data. The behaviour of many systems can be described by an s-domain or z-domain transfer function model, at least for a given excitation amplitude range. The quality of the fit can be assessed by the analysis of the residuals, that is, of the difference between the measured data and the model.However, even slight nonlinearities can be misleading, by causing part of the residuals non-explicable by the linear model. We cannot simply tell if the excess residual error is due to undermodelling or to nonlinear system behaviour. This can lead to erroneous overmodelling. Therefore, characterisation of the nonlinear system behaviour is essential in the verification of linear models.The Frequency Domain System Identification Toolbox has been extended with analysis tools of nonlinear system behaviour. Specially designed excitation signals allow the description of nonlinearity levels. By this, model verification becomes possible even if nonlinear error terms excess linear additive noise.

Frequency domain system identification for controlled civil engineering structures

Controlling buildings, towers, and other civil engineering structures for active vibration mitigation is a rapidly growing field of control systems technology. Of fundamental importance in the development of feedback control laws it is to identify the inherent dynamic characteristics of such control systems with suitable mathematical models. This brief contributes to this research field by first recognizing the existence of fixed zero dynamics in the control input channels. The discovery is subsequently incorporated into the development of specialized frequency domain identification algorithms, which also address the constrained stability of the identified model. Finally, a practical case study is presented to illustrate the important aspects of frequency domain modeling of controlled structures.

Fourier fringe processing using a regressive Fourier-transform technique

Since the introduction of a fourier fringe algorithm by Takeda, it has been possible to determine the phase of a particular light source impinging on an object from one sole image. This has led to applications in many whole field optical measurement techniques such as ESPI, holography, profilometry and so on. However, the basic processing technique, in case of the 2D-Fourier transform, is subject to a major drawback. Because this technique supposes periodicity in a fringe image, the so-called leakage effects occur. This gives rise to non-negligible errors, which can be resolved by using a regressive Fourier transformation technique. In the method introduced in this article, the fringe signal is represented by a model using sines and cosines where the frequency is not fixed (which is the case for classical FFT-techniques). The coefficients of those sines and cosines together with the frequency components are then estimated locally by means of a frequency domain system identification technique. This allows the fringe pattern to be unwrapped without any distortion. This method will be applied in particular to Fourier-transform profilometry (determines object geometry using shifts of projected fringes) although it can be used in any of the techniques mentioned above. Moreover, it will be shown that the proposed method can deal with other distortions that occur in practice such as over-modulation and varying fringe visibility. The proposed technique will be validated on both simulations and on a profile measurement of a pipe section.

AN INDUSTRIAL REHEATING FURNACE WITH FLUE GAS RECIRCULATION MODELED BY LINEAR TRANSFER FUNCTIONS

To design an effective active combustion control system, it is important to have detailed knowledge about the dynamic relationships of the furnace from its inputs to its outputs. A novel approach has been proposed to construct a set of dynamic models in the form of transfer functions for an industrial furnace with flue gas recirculation (FGR) based on the computational fluid dynamics (CFD) simulation results. The inputs to the furnace are the flow rate of the combustion air, the temperature of the combustion air, and the pressure head of the FGR fan. The outputs are nitric oxide (NO) and oxygen (O2) concentrations. Therefore, the furnace has been represented by a three-input and two-output system. The model construction relies on the CFD simulations of the combustion process and NO formation in the furnace as well as frequency domain system identification techniques. Low-amplitude sinusoidal signals of different frequencies have been administered at the furnace inputs around a designed furnace operating condition. The dynamic relationships among the furnace inputs and outputs at these frequencies are first established in terms of frequency responses. These frequency responses are further processed by a least-squares-based system identification technique to convert them to a set of parametric models. These models are validated against the results obtained from the CFD simulations.

Rapid Frequency-Domain Modeling Methods for Unmanned Aerial Vehicle Flight Control Applications

Modeling of the flight dynamics of unmanned aerial vehicles (UAVs) poses unique challenges that are not present with manned aircraft. The use of analytical modeling methods based on first principles is often difficult for UAVs because of short design cycles, reduced development costs, and many unconventional designs. Also, without the need to carry a pilot, UAVs are often much smaller and lighter than manned aircraft. The lower weights and inertias result in higher natural frequencies and quicker vehicle responses requiring high bandwidth dynamics models. Frequency-domain system identification is especially well suited to the modeling of UAVs. With the availability of flight hardware early in many UAV programs, dynamic response models of the vehicle can be identified and validated rapidly with flight data. The system identification method also allows for rapid updating of vehicle response models as physical changes are made to the vehicle configuration. The use of frequency-domain system identification in the development and operation of a number of UAV programs is discussed. The example aircraft programs include Northrop Grumman’s Fire Scout vertical takeoff unmanned air vehicle demonstrator based on the Schweizer 300

Unsteady aerodynamic model of a cargo container for slung-load simulation

AbstractThe problem of simulation models capable of predicting the aerodynamic instability of helicopter slung-load cargo containers and bluff bodies is addressed. Instability for these loads is known to depend on unsteady frequency-dependent aerodynamics, but simulation models that include the unsteady aerodynamics do not currently exist. This paper presents a method for generating such models using computational fluid dynamics (CFD) to generate forced-oscillation aerodynamic data and frequency domain system identification techniques to generate a frequency response from the CFD data and to identify a transfer function fit to the frequency response. The method is independent of the responsible flow phenomenon and is expected to apply to bluff-bodies generally. Preliminary results are presented for the case of the 6- by 6- by 8-ft CONEX (container express) cargo container. The present work is based on two-dimensional (2D) aerodynamic data for the CONEX side force and yaw moment generated by a forced oscillation in which frequency is varied smoothly over the range of interest. A first-order rational polynomial transfer function is found adequate to fit the aerodynamics, and this is shown to provide a good match with flight test data for the yawing motion of the CONEX.

Orthogonal basis functions in discrete least-squares rational approximation

We consider a problem that arises in the field of frequency domain system identification. If a discrete-time system has an input–output relation Y( z)= G( z) U( z), with transfer function G, then the problem is to find a rational approximation G ̂ n for G. The data given are measurements of input and output spectra in the frequency points z k : { U( z k ), Y( z k )} k=1 N together with some weight. The approximation criterion is to minimize the weighted discrete least squares norm of the vector obtained by evaluating G− G ̂ n in the measurement points. If the poles of the system are fixed, then the problem reduces to a linear least-squares problem in two possible ways: by multiplying out the denominators and hide these in the weight, which leads to the construction of orthogonal vector polynomials, or the problem can be solved directly using an orthogonal basis of rational functions. The orthogonality of the basis is important because if the transfer function G ̂ n is represented with respect to a nonorthogonal basis, then this least-squares problem can be very ill conditioned. Even if an orthogonal basis is used, but with respect to the wrong inner product (e.g., the Lebesgue measure on the unit circle) numerical instability can be fatal in practice. We show that both approaches lead to an inverse eigenvalue problem, which forms the common framework in which fast and numerically stable algorithms can be designed for the computation of the orthonormal basis.

Design of accelerometer layout for structural monitoring and damage detection

The paper presents an algorithm for designing a layout of accelerometers for structural monitoring and damage detection. The maximum likelihood approach has been applied as a mathematical basis for the algorithm. Fisher information matrix is formulated in terms of mode shape sensitivity with respect to structural parameters. A scheme of an effective independence distribution vector has been applied to determine optimal locations of accelerometers. Singular value decomposition scheme has been applied to overcome the rank deficiency problem in the computed sensitivity matrix. The adequacy of the proposed algorithm has been examined by estimating structural parameters through a frequency-domain system identification. The identification results using the response data measured at the locations selected by the proposed algorithm are compared with those at arbitrary locations. In addition to the design of accelerometer layout for a structural monitoring of general purpose, the paper proposes another algorithm of layout design for damage detection with the assumption that some members critical for the structural safety are pre-determined. Damage possibility of each member computed from the static strain energy has been implemented as a weighting factor in the algorithm. Simulation studies have been carried out on a two-span multigirder bridge to examine the proposed algorithms.

Applying system identification to assess the vibro-acoustic behaviour of airplanes

Effective aircraft interior noise reduction measures require an in-depth understanding of the operational noise and vibration fields as well as the intrinsic system characteristics. The former requires detailed mapping of the in-flight sound and vibration responses, whereas the latter requires the proper modelling of the vibro-acoustic system behaviour. The latter is discussed in this paper where frequency-domain system identification is applied to acoustical transfer functions, measured in a fully-trimmed aircraft cavity.

Spatial system identification of a simply supported beam and a trapezoidal cantilever plate

Dynamic models of structural and acoustic systems are usually obtained by means of either modal analysis or finite element modeling. Detrimentally, both techniques rely on a comprehensive knowledge of the system's physical properties. As a consequence, experimental data and a nonlinear optimization are required to refine the model. For the purpose of control, system identification is often employed to estimate the dynamics from disturbance and command inputs to set of outputs. Such discretization of a spatially distributed system places unknown weightings on the control objective, in many cases, contradicting the original goal of optimal control. This paper introduces a frequency domain system identification technique aimed at obtaining spatially continuous models for a class of distributed parameter systems. The technique is demonstrated by identifying a simply supported beam and a trapezoidal cantilever plate, both with bonded piezoelectric transducers. The plate's dimensions are based on the scaled side elevation of a McDonnell Douglas FA-18 vertical stabilizer.

Frequency Domain System Identification Toolbox for MATLAB: Automatic Processing - from Data to Models

The Frequency Domain System Identification Toolbox for MATLAB is an effective tool for the identification of linear dynamic system models from measured data. Since the use of advanced system identification methods often requires a lot of programming work, the attention can be deflected from the modelling issues. Therefore, a Graphical User Interface (GUI) was developed which allows the experimenter to visually follow and control the data processing and modelling steps.However, for many users it is still desirable to obtain good models with as few decisions to be made as it is possible. Therefore, automatic processing steps have been added to the GUI. Identification can be done now in this toolbox with a minimum of user interactions in the graphics windows, and a reasonable model is returned, ready for control or physical analysis.

Flight flutter analysis using frequency-domain system identification techniques

In this paper frequency-domain estimators will be presented for application in the field of flight flutter analysis. Flight flutter tests are expensive and not without risks even when approached with caution. The complete session of flight tests must be as fast as possible but this often results in low quality data. Dedicated frequency-domain estimators will be presented to estimate and track the modal parameters as a function of the flight conditions.

Frequency-Domain System Identification Techniques for Experimental and Operational Modal Analysis

In this paper frequency-domain estimators will be presented for application in the field of modal analysis. In "Experimental Modal Analysis" system identification is used to model mechanical systems with a few inputs and hundreds of outputs. This requires adapted estimators designed to handle large amount of data in a reasonable amount of time. Next, attention will be paid to "Operational Modal Analysis" and it will be shown how the modal parameters can be estimated from output-only data. Finally, a combined experimental/operational identification approach will be introduced.

Wavelet Transforms for System Identification in Civil Engineering

Abstract: The time‐frequency character of wavelet transforms allows adaptation of both traditional time and frequency domain system identification approaches to examine nonlinear and non‐stationary data. Although challenges did not surface in prior applications concerned with mechanical systems, which are characterized by higher frequency and broader‐band signals, the transition to the time‐frequency domain for the analysis of civil engineering structures highlighted the need to understand more fully various processing concerns, particularly for the popular Morlet wavelet. In particular, as these systems may possess longer period motions and thus require finer frequency resolutions, the particular impacts of end effects become increasingly apparent. This study discusses these considerations in the context of the wavelet's multi‐resolution character and includes guidelines for selection of wavelet central frequencies, highlights their role in complete modal separation, and quantifies their contributions to end‐effect errors, which may be minimized through a simple padding scheme.

Generalization of a total least squares problem in frequency-domain system identification

In this paper, a solution to the frequency-domain system identification of a linear time-invariant system is investigated. A generalization of the total least squares algorithm is shown and analyzed. Some simulation examples on real measured data are given, in order to illustrate the properties of the new method in practice.

Fueling Control of Spark Ignition Engines

Presented in this paper is an adaptive, model based, fueling control system for spark ignition-internal combustion engines. Since the fueling control system is model based, the engine maps currently used in engine fueling control are eliminated. This proposed fueling control system is modular and can therefore accommodate changes in the engine sensor set such as replacing the mass-air flow sensor with a manifold air pressure sensor. The fueling algorithm can operate with either a switching type O 2 sensor or a linear O 2 sensor. The fueling control system is also parceled into steady state fueling compensation and transient fueling compensation. This feature provides the distinction between fueling control adaptation for transient fueling and steady state fueling. The steady state fueling compensation utilizes a feedforward controller which determines the necessary fuel pulsewidth after a throttle transient to achieve stoichiometry. This feedforward controller is comprised of two nonlinear models capturing the steady state characteristics of the fueling process. These models are identified from an input-output testing procedure where the inputs are fuel pulsewidth and mass-air flow signal and the output is a lambda signal. These models are adapted via a recursive least squares method to accommodate product variability, engine aging, and changes in the operating environment. The transient fueling compensation also utilizes a feedforward controller that captures the essential dynamic characteristics of the transient fueling operation. This controller is measured using a frequency domain system identification approach. This proposed fueling control system is demonstrated on a Ford 4.6L V-8 fuel injected engine.

OPTIMAL MODEL FOR THE DIFFRACTION EFFECT IN THE ULTRASONIC FIELD OF PISTON TRANSDUCERS

In this work, the analytical and experimental examination of the problem of diffraction effect is treated. In the laboratory, the diffraction phenomena have been mainly due to the beam spread of the ultrasonic plane wave propagating through a viscoelastic material. In fact, this effect has been found to be related, essentially to the attenuation and dispersion losses on a viscoelastic material. In this work, a frequency domain system identification approach is applied to determine an optimal function correcting the beam spread effect in both the normal and oblique incidences for a large frequency band (300 kHz–3 MHz). The Maximum Likelihood Estimator is applied to the magnitude and phase of the measured beam patterns of the used transducers in order to determine the model parameters. The calibration procedure is also discussed. Once the proposed model is established, the propagation through a viscoelastic plate is described and a comparison with measurements is done to validate the investigated model. The obtained longitudinal and shear attenuation and dispersion of the ultrasound in the viscoelastic plate are compared with those obtained by applying the complex harmonic plane waves combination model.

Two-dimensional frequency-domain blind system identification using higher order statistics with application to texture synthesis

In this paper, Shalvi and Weinstein's (1993) super-exponential (SE) algorithm using higher order statistics for blind deconvolution of one-dimensional (1-D) linear time-invariant systems is extended to a two-dimensional (2-D) SE algorithm. Then, a 2-D frequency-domain blind system identification (BSI) algorithm for 2-D linear shift-invariant (LSI) systems using the computationally efficient 2-D SE algorithm and the 2-D linear prediction error filter is proposed. In addition to the LSI system estimate, the proposed BSI algorithm also provides a minimum mean square error (MMSE) equalizer estimate and an MMSE signal enhancement filter estimate. Then, a texture synthesis method (TSM) using the proposed BSI algorithm is presented. Some simulation results to support the efficacy of the proposed BSI algorithm and some experimental results to support the efficacy of the proposed TSM are presented. Finally, some conclusions are drawn.

Experimental validation for the diffraction effect in the ultrasonic field of piston transducers and its influence on absorption and dispersion measurements.

The aim of this work was to study the diffraction effects in the ultrasonic field of piston source transducers and their importance for accurate measurements of attenuation and dispersion in viscoelastic materials. In laboratory measurements, the diffraction phenomena are mainly due to the beam spread of the ultrasonic wave propagating in viscoelastic materials. This effect is essentially related to the estimated attenuation and dispersion in the material. In this work, a frequency domain system identification approach, using the maximum likelihood estimator (MLE), was applied to the measured data in order to determine a function for correcting the diffraction losses in both normal and oblique incidences for a large frequency band (300 kHz to 3 MHz). The effective radius of the used transmitter was determined by the inverse problem when ultrasonic beam propagation was investigated in a water medium. Using the estimated radius, the propagation through viscoelastic materials was established, and the acoustic parameters of these materials were estimated. Attention was paid to the determination of the attenuation and dispersion in the materials. These quantities were compared to those obtained without diffraction correction in order to see the influence of introducing the diffraction correction into the propagation model.